Approximate solution by the straight line method of a partial differential equation of the first elliptic type

1964 ◽  
Vol 4 (3) ◽  
pp. 272-281
Author(s):  
E.O. Omarov
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Elliptic Type ◽  
Partial Differential ◽  
Line Method ◽  
Straight Line ◽  
Straight Line Method

Electrostatics in a gravitational field

1978 ◽  
Vol 80 (3-4) ◽  
pp. 201-211 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Gravitational Field ◽  
Closed Form ◽  
Electrostatic Potential ◽  
Point Charge ◽  
Elementary Solution ◽  
Elliptic Type ◽  
Partial Differential

SynopsisIn this paper, the electrostatic potential of a point charge in a Reisser-Nordström gravitational field is found in closed form by using the theory of Hadamard's elementary solution of a partial differential equation of elliptic type.

scholarly journals A Stable Difference Scheme for a Third-Order Partial Differential Equation

2018 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
A Ashyralyev ◽  
Kh Belakroum
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.

scholarly journals On the behaviour near the boundary of solutions of a semi-linear partial differential equation of elliptic type

1981 ◽  
Vol 31 (4) ◽  
pp. 405-414
Author(s):  
J. Chabrowski ◽  
B. Thompson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Sobolev Space ◽  
Linear Partial Differential Equation ◽  
Elliptic Type ◽  
Partial Differential

AbsrtactThe purpose of this note is to investigate traces of the functions In(1 +|u|), where u is a solution of a semi-linear partial differential equation of elliptic type, belonging to an appropriate Sobolev space. This article complements the results of Chabrowski and Thompson (1980), and Mihailov (1972), (1976).

Tikhonov Regularization Solve Partial Differential Equations Inverse Problem

2011 ◽  
Vol 50-51 ◽  
pp. 459-462
Author(s):  
Ya Li He ◽  
Shi Qiu Zheng ◽  
Yan Mei Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
General Theory ◽  
Tikhonov Regularization ◽  
Related Concept ◽  
Partial Differential ◽  
Well Posed

This article discussed the partial differential equation inverse problem. Because the partial differential equation inverse is the misalignment improperly posed problem, therefore analyzed has had the improperly posed reason. To process the partial differential equation inverse correctly not well-posed ness this difficulty, obtains relies on continuously the data stable approximate solution, has drawn support from the regularization related concept and the regularization general theory.

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